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Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.
- a)350π2
- b)750π
- c)1000π
- d)3000
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider steady, one-dimensional compressible flow of a gas in a pipe ...
Given;
Diameter (d ) = 1 m
Density (ρ)= 1kg/m3
Velocity (V1 ) = 100 m/s V
elocity (V2 ) = 170 m/s
Pressure drop between two location =10 kPa
Force exerted by the gas on the pipe between two locations is
Hence, the correct option is (B).
Diameter (d ) = 1 m
Density (ρ)= 1kg/m3
Velocity (V1 ) = 100 m/s V
elocity (V2 ) = 170 m/s
Pressure drop between two location =10 kPa
Force exerted by the gas on the pipe between two locations is
Hence, the correct option is (B).
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Community Answer
Consider steady, one-dimensional compressible flow of a gas in a pipe ...
To find the force exerted by the gas on the pipe, we can use the momentum equation for steady, one-dimensional compressible flow:
ΔP = ρ * Δv * A
Where:
ΔP = pressure drop (Pa)
ρ = density (kg/m^3)
Δv = change in velocity (m/s)
A = cross-sectional area of the pipe (m^2)
First, let's calculate the change in velocity (Δv) between the two locations:
Δv = v2 - v1
Δv = 170 m/s - 100 m/s
Δv = 70 m/s
Next, we need to calculate the cross-sectional area of the pipe (A). The pipe diameter is given as 1 m, so the radius (r) is 0.5 m:
A = π*r^2
A = π*(0.5 m)^2
A = π*0.25 m^2
A = 0.7854 m^2
Now, let's substitute the given values into the momentum equation:
ΔP = ρ * Δv * A
10,000 Pa = 1 kg/m^3 * 70 m/s * 0.7854 m^2
To solve for the density (ρ), we can rearrange the equation:
ρ = ΔP / (Δv * A)
ρ = 10,000 Pa / (70 m/s * 0.7854 m^2)
ρ ≈ 179.9 kg/m^3
Finally, we can calculate the force exerted by the gas on the pipe using the equation:
Force = ρ * A * Δv
Force = 179.9 kg/m^3 * 0.7854 m^2 * 70 m/s
Force ≈ 9,445.2 N
Therefore, the force exerted by the gas on the pipe between these two locations is approximately 9,445.2 N.
ΔP = ρ * Δv * A
Where:
ΔP = pressure drop (Pa)
ρ = density (kg/m^3)
Δv = change in velocity (m/s)
A = cross-sectional area of the pipe (m^2)
First, let's calculate the change in velocity (Δv) between the two locations:
Δv = v2 - v1
Δv = 170 m/s - 100 m/s
Δv = 70 m/s
Next, we need to calculate the cross-sectional area of the pipe (A). The pipe diameter is given as 1 m, so the radius (r) is 0.5 m:
A = π*r^2
A = π*(0.5 m)^2
A = π*0.25 m^2
A = 0.7854 m^2
Now, let's substitute the given values into the momentum equation:
ΔP = ρ * Δv * A
10,000 Pa = 1 kg/m^3 * 70 m/s * 0.7854 m^2
To solve for the density (ρ), we can rearrange the equation:
ρ = ΔP / (Δv * A)
ρ = 10,000 Pa / (70 m/s * 0.7854 m^2)
ρ ≈ 179.9 kg/m^3
Finally, we can calculate the force exerted by the gas on the pipe using the equation:
Force = ρ * A * Δv
Force = 179.9 kg/m^3 * 0.7854 m^2 * 70 m/s
Force ≈ 9,445.2 N
Therefore, the force exerted by the gas on the pipe between these two locations is approximately 9,445.2 N.
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Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer?
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Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer?.
Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.a)350π2b)750πc)1000πd)3000Correct answer is option 'B'. Can you explain this answer?.
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